Longitudinal logistic regression with continuous-time first-order autocorrelation structure

Hi Dennis,

Another way to go would be to include a random intercept and a random 
time effect (both over persons) in the logit, much like is done in 
linear models. This creates correlation between logit values across 
successive time-points. This is e.g. explained in Snijders and Bosker's 
book  and in Singer and Willett. You can make the model increasingly 
more flexible (in terms of the correlation structure over time) by not 
only including a linear random time effect but also a quadratic, cubic 
etc. time-effect. This is a different approach than letting the error 
terms "e" correlate over time. But it serves the same end: correlation 
over time.

I think there's nothing wrong with this "multilevel growth model" 
approach for a glm, but anyone please correct me if  I'm wrong. Anyway, 
it can be carried with most multilevel or random effects software 
packages, like glmer in R.

Best regards, Ben.

Dear All.

I need to analyze an intensive longitudinal data set with a binary outcome
variable. In the ?Ecological Momentary Assessment? (EMA) study,
participants received five random prompts per day for six weeks, asking
them (among other things) whether they were craving a particular drug
(yes/no). At the most basic level, I want to know whether the likelihood of
craving the drug changed across time.

Given the variable time intervals of measurement and many missing data
points, a continuous-time first-order autocorrelation model seems
necessary.

I found tutorials on how to allow for continuous-time autocorrelation and
missing data in an LMM, using nlme::lme and corCAR1, but I am at a loss as
to what to do in a GLMM.

I would be thankful for any suggestions on how to analyze this kind of data
in R.

Dennis

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